الصفحة 6
الصفحة 6
Artinian Modules over Group Rings
This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.
Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach
Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory.
Application of numerical methods in engineering problems using MATLAB
Presents an analysis of structures using numerical methods and mathematical modeling. This structural analysis also includes beam, plate, and pipe elements, and examines deflection and frequency or buckling loads. The various engineering theories of beams/plates/shells are comprehensively presented, and the relationships between stress and strain, and the governing equations of the structure are extracted. To solve governing equations with numerical methods, there are two general types, including methods based on derivatives or integrals. Derivative-based methods have the advantage of flexibility in modeling boundary conditions, low analysis time, and a very high degree of accuracy.
Analyzing uncertainty in civil engineering
This volume addresses the issue of uncertainty in civil engineering from design to construction. Failures do occur in practice. Attributing them to a residual system risk or a faulty execution of the project does not properly cover the range of causes. A closer scrutiny of the adopted design, the engineering model, the data, the soil-construction-interaction and the model assumptions is required. Usually, the uncertainties in initial and boundary conditions are abundant. Current engineering practice often leaves these issues aside, despite the fact that new scientific tools have been developed in the past decades that allow a rational description of uncertainties of all kinds, from model uncertainty to data uncertainty. It is the aim of this volume to have a critical look at current engineering risk concepts in order to raise awareness of uncertainty in numerical computations, shortcomings of a strictly probabilistic safety concept, geotechnical models of failure mechanisms and their implications for construction management, execution, and the juristic question of responsibility. In addition, a number of the new procedures for modelling uncertainty are explained.
Analysis of Low-Speed Unsteady Airfoil Flows
This book provides an introduction to unsteady aerodynamics with emphasis on the analysis and computation of inviscid and viscous two-dimensional flows over airfoils at low speeds. It begins with a discussion of the physics of unsteady flows and an explanation of lift and thrust generation, airfoil flutter, gust response and dynamic stall. This is followed by an exposition of the four major calculation methods in currents use, namely inviscid-panel, boundary-layer, viscous-inviscid interaction and Navier-Stokes methods. Undergraduate and graduate students, teachers, scientists and engineers concerned with aeronautical, hydronautical and mechanical engineering problems will gain understanding of the physics of unsteady low-speed flows and an ability to analyze these flows with modern computational methods.
Analyse asymptotique et couche limite = Asymptotic analysis and boundary layer
The aim of the book is to give teachers and students (from Bac + 4) in applied mathematics and fluid mechanics a teaching and learning tool illustrated by fifty problems accompanied by their detailed correction. This book presents a new method of asymptotic analysis for "boundary layer" problems. This is called MASC "Method of Complementary Successive Approximations". The first half of the book is devoted, in addition to the presentation of the MASC, to organize the knowledge necessary for the asymptotic analysis and to give the keys allowing the understanding of what is a problem called "boundary layer" and the methods allowing. to build an approximation. The second part is devoted to the application of MASC in fluid mechanics and to the comparison with the more traditional methods resulting from the famous MDAR, "Method of Connected Asymptotic Developments".
An Introduction to Ordinary Differential Equations
This textbook provides a rigorous and lucid introduction to the theory of ordinary differential equations (ODEs), which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines.
An Introduction to Meshfree Methods and Their Programming
This book aims to present meshfree methods in a friendly and straightforward manner, so that beginners can very easily understand, comprehend, program, implement, apply and extend these methods. It provides first the fundamentals of numerical analysis that are particularly important to meshfree methods. Typical meshfree methods, such as EFG, RPIM, MLPG, LRPIM, MWS and collocation methods are then introduced systematically detailing the formulation, numerical implementation and programming. Many well-tested computer source codes developed by the authors are attached with useful descriptions. The application of the codes can be readily performed using the examples with input and output files given in table form. These codes consist of most of the basic meshfree techniques, and can be easily extended to other variations of more complex procedures of meshfree methods. Readers can easily practice with the codes provided to effective learn and comprehend the basics of meshfree methods.
An introduction to differential geometry with applications to elasticity
Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory.
Algebraic Analysis of Differential Equations : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai Editors
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas, providing interested researchers and students with valuable suggestions and instructive guidance for their work.
Air-Ice-Ocean Interaction : Turbulent Ocean Boundary Layer Exchange Processes
At a time when the polar regions are undergoing rapid and unprecedented change, understanding exchanges of momentum, heat and salt at the ice-ocean interface is critical for realistically predicting the future state of sea ice. By offering a measurement platform largely unaffected by surface waves, drifting sea ice provides a unique laboratory for studying aspects of geophysical boundary layer flows that are extremely difficult to measure elsewhere. This book draws on both extensive observations and theoretical principles to develop a concise description of the impact of stress, rotation, and buoyancy on the turbulence scales that control exchanges between the atmosphere and underlying ocean when sea ice is present. Several interesting and unique observational data sets are used to illustrate different aspects of ice-ocean interaction ranging from the impact of salt on melting in the Greenland Sea marginal ice zone, to how nonlinearities in the equation of state for seawater affect mixing in the Weddell Sea.
A Posteriori Error Analysis Via Duality Theory : With Applications in Modeling and Numerical Approximations
This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates.
A Modern Theory of Factorial Design
Factorial design plays a fundamental role in efficient and economic experimentation with multiple input variables and is extremely popular in various fields of application, including engineering, agriculture, medicine and life sciences. Factorial experiments are often used in case studies in quality management and Design for Six Sigma (DFSS).Factorial design plays a fundamental role in efficient and economic experimentation with multiple input variables and is extremely popular in various fields of application, including engineering, agriculture, medicine and life sciences. Factorial experiments are often used in case studies in quality management and Design for Six Sigma (DFSS).
